Measurement of $CP$ violation of neutral kaon system in $J\mathrm{/}\psi$ decay at the Super Tau-Charm Facility

In this paper, we present a preliminary study of $CP$ violation effect of $K^0-{\bar{K}}^0$ system in $J\mathrm{/}\psi$ decay. The $CP$ violation parameters ${\eta }_{+-}$ and ${\eta }_{00}$ as well as their corresponding phase ${\phi }_{+-}$ and ${\phi }_{00}$ can be determined by the difference of the time-dependent decay rates between $K^0$ and ${\bar{K}}^0$ produced from $J\mathrm{/}\psi \to K^{-}{\pi }^{+}{K}^0+c\mathrm{.}c\mathrm{.}$ processes. We investigate the precisions of the measurements of the CP violation effect at the Super Tau-Charm facility(STCF), a $e^{+}{e}^{-}$ collider with a peak luminosity of $0.5\times {10}^{35}{\mathrm{c}\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$. The parameters ${\eta }_{+-}$ and its phase ${\phi }_{+-}$ can be measured at a relative precision of $1\times {10}^{-3}$, which the statistical accuracy will be several times better than that of the existing PDG average values.